Probabilistic Modeling with Matrix Product States

Abstract

Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable effective models, is a modification of the density matrix renormalization group procedure adapted for learning a probability distribution. The conclusion that circuit-based models offer a useful inductive bias for classical datasets is supported by experimental results on the parity learning problem.

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Cited by in corpus (15)

• Machine learning and the physical sciences
• Differentiable Programming Tensor Networks
• Machine Learning for Quantum Matter
• An end-to-end trainable hybrid classical-quantum classifier
• Modeling Sequences with Quantum States: A Look Under the Hood
• Natural evolution strategies and variational Monte Carlo
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization
• Differentiable Programming of Isometric Tensor Networks
• Explainable Natural Language Processing with Matrix Product States
• Language Modeling with Reduced Densities
• Tensor Networks for Probabilistic Sequence Modeling
• Deep tensor networks with matrix product operators
• Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework
• Quantum Tensor Networks, Stochastic Processes, and Weighted Automata
• SchrödingeRNN: Generative Modeling of Raw Audio as a Continuously Observed Quantum State